J. Phys. Chem. B 2000, 104, 12079-12083
12079
Kinetic Analysis of Fast Hydrogenase Reaction of DesulfoWibrio Wulgaris Cells in the Presence of Exogenous Electron Acceptors Hirosuke Tatsumi, Kenji Kano, and Tokuji Ikeda* DiVision of Applied Life Sciences, Graduate School of Agriculture, Kyoto UniVersity, Sakyo-ku, Kyoto 606-8502, Japan ReceiVed: July 12, 2000; In Final Form: October 6, 2000
DesulfoVibrio Vulgaris (Hildenborough) cells catalyzed the oxidation of hydrogen with several quinone compounds as exogenous electron acceptors, in which hydrogenase existing in the periplasmic space of the bacterial cells functioned as the enzyme to catalyze the reaction. The rates of the hydrogen oxidation and quinone reduction were analyzed by a Michaelis-Menten type equation to yield the values of the catalytic constant of a D. Vulgaris cell, kB,cat, and the bimolecular reaction rate constants for hydrogen, kB,cat/KB,H, and for quinone, kB,cat/KB,Q. They were in the ranges of kB,cat ) (1.1-5.3) × 107 s-1, kB,cat/KB,H ) (1.8-2.2) × 1012 M-1 s-1 and kB,cat/KB,Q ) (0.97-10) × 1010 M-1 s-1 for the reactions with four kinds of quinone compounds. The mass transfer process involved in the bacterial cell-catalyzed reaction was considered by a model taking account of the substrate diffusion to and through the cross-membrane channels (composed of proteins called porins) distributed in the bacterial outer membrane to reach the periplasmic space. The rate of diffusion of the substrates toward the whole cell surface was also calculated on the basis of the model of spherical diffusion and compared with the rate of the diffusion through the cross-membrane channels. Calculation based on the model has revealed that the diffusion toward the cell surface is the slowest step of the mass transfer processes and that the rates of the catalytic reaction are large enough to be close to the rates of the substrate diffusion.
Introduction Hydrogenase reaction has attracted considerable interest both for the novel chemistry involved and the potential application in fuel cell systems because of the high catalytic activity for the redox reaction H+ + e- a 1/2H2 in the presence of suitable electron donors/acceptors. Hydrogenases exist in a wide range of both bacterial and algal species, and function in vivo to either evolve or consume H2.1 Kinetic measurements of the hydrogenase reaction have mostly been done with the enzymes isolated from DesulfoVibrio species by electrochemical methods based on enzymatic electrocatalysis.2-7 The second-order rate constants in the range from 7 × 107 to 3 × 108 M-1 s-1 have been reported for the electron transfer from hydrogenase to cytochrome c32-5 and 2 × 108 M-1 s-1 from hydrogenase to cytochrome c553.5 The rate constants in the range from 105 to 106 M-1 s-1 have been reported for the electron transfer from cytochrome c3 to hydrogenase6 and 104 M-1 s-1 from ferredoxin II to hydrogenase6 and from 106 to 107 M-1 s-1 from viologen dyes to hydrogenase.7 Butt et al. have reported direct electrochemistry of hydrogenase from Megasphaera elsdenii, producing a reversible catalytic current in the presence of H2 in accord with a very fast electron-transfer reaction between hydrogenase and H+/H2.8 We have measured for the first time the rate of the hydrogenase reaction of whole D. Vulgaris cells with methyl viologen as an exogenous electron carrier and shown that the whole cell-catalyzed hydrogenase reaction is as fast as those catalyzed by isolated hydrogenases.9 D. Vulgaris cells produce a reversible catalytic current in the presence of H2 with methyl * Corresponding author. Fax: +81-75-753-6456. E-mail: tikeda@ kais.kyoto-u.ac.jp.
viologen as an electron-transfer mediator between the electrode and the bacterial cells.9 Such high catalytic activity of the whole bacterial cells is amazing in view of the fact that the substrates must be supplied from the outside of the cells through the outer membrane to reach the periplasmic space where the catalytic reaction takes place. The present paper deals with this mass transfer problem. The H2 oxidation reaction catalyzed by D. Vulgaris (strain Hildenborough) cells has been measured with quinone compounds as exogenous electron acceptors. Periplasmic hydrogenase is the enzyme to which the bacterial catalytic activity is attributed.9 The quinone compounds have redox potentials more positive than those of viologen dyes; thus we may expect one-way catalytic electron transfer from H2 to the quinone compounds with little effect of the backward reaction.10 This allows the use of ordinary equations of enzyme kinetics and enzyme electrocatalysis for the kinetic analysis of the bacterial cellcatalyzed H2 oxidation reaction. The results are fully discussed with reference to the effect of mass transfer rates to and through the bacterial outer membrane and toward the cell surface. Experimental Section Chemicals. 1,4-Naphthoquinone (NQ) was purchased from Wako Chemical Co., 2-methyl-1,4-naphthoquinone (vitamin K3, VK3) and anthraquinone 2-sulfonate sodium salt (AQS) were from Nakalai Tesque Inc., and 2,6-dimethyl-1,4-benzoquinone (DMBQ) was from TCI Co. All the quinone compounds were used as received. Other chemicals were purchased from Wako Chemical Co. and used without further purification. Cell Cultivation, Storage, and Preparation of the Cell Suspension. DesulfoVibrio Vulgaris (Hildenborough) (D. Vul-
10.1021/jp002475i CCC: $19.00 © 2000 American Chemical Society Published on Web 11/28/2000
12080 J. Phys. Chem. B, Vol. 104, No. 50, 2000 garis (H)) cells were anaerobically cultured and harvested as described previously.9 The harvested cells were suspended in a saline solution (0.85% NaCl), and the suspension was stored in a vial kept anaerobic at 5 °C and used within a few days. A portion of the suspension was injected into a phosphate buffer (pH 7.0) and incubated under H2 bubbling for 40 min before kinetic measurements. Periplasmic hydrogenase of D. Vulgaris (H) once exposed to air is known to require preincubation under the atmosphere of H2 to recover the activity.11,12 We confirmed that 40 min was enough for the D. Vulgaris (H) cells to recover the full hydrogenase activity by the electrocatalysis measurement using the D. Vulgaris (H)-modified electrode.10 The cell population in the suspension was determined by using a hemacytometer; the suspension at unit absorbance (610 nm) contained 2.9 × 108 cells per cm3, that is, the concentration of the bacterial cell [B] was 4.8 × 10-13 M. Measurements of H2 Oxidation Rate. An anodic current due to the electrochemical oxidation of H2 was measured in an airtight cell with a Clark-type oxygen electrode fixed at 0.6 V vs Ag|AgCl (saturated KCl).13 The current was calibrated with the H2 concentration 0.78 mM14 in the solution bubbled with H2 gas at an atmospheric pressure at 25 °C. The electrode was immersed in a bacterial suspension that had been bubbled with a mixture of H2 and Ar gases in a given volume ratio to measure an anodic current. The current started to decrease on the addition of a quinone compound to the suspension; the H2 oxidation rate was measured from the initial slope of the current decay. Measurements of Quinone Reduction Rate. The rate of quinone reduction was measured by the method based on the catalytic current produced by the bacterial cell-catalyzed oxidation of H2. A glassy carbon electrode (3 mm i.d., BAS Co.) was immersed in a bacterial suspension saturated with H2 gas to record chronoamperograms. First, a cathodic current at a fixed potential was recorded to measure the current for the reduction of a quinone compound added to the suspension. After the cathodic current decreased to almost zero, the electrode potential was stepped to a positive potential to record the anodic catalytic current for quinone-mediated bacterial cell-catalyzed oxidation of H2.15,16 All the electrochemical measurements were performed on a BAS CV-50W voltammetric analyzer with a three-electrode system using an Ag|AgCl (saturated KCl) electrode and a Pt disk electrode as the reference and counter electrodes, respectively. All measurements were done at 25 °C. Results Dependence of the Catalytic Reaction Rate on the Concentration of H2. The concentration of H2 in a D. Vulgaris (H) cell suspension, [H2], was measured as an anodic current at a Clark-type oxygen electrode as described in the Experimental Section. Figure 1A illustrates an example of the current, which begins to decrease by the addition of VK3 to almost zero. The result indicates that H2 in the suspension is completely consumed by the D. Vulgaris (H) cell using VK3 as an electron acceptor. The rate of the bacterial cell catalysis, V, for the oxidation of H2 with VK3 was measured as the initial slope of the currenttime curve. The rate was proportional to the concentration of the bacterial cell [B] in the range between 5.0 × 10-14 and 2.5 × 10-13 M and was almost independent of the VK3 concentration [VK3] at [VK3] g 1.4 mM. The value of V increased with increasing [H2] to approach a saturation value as illustrated in Figure 1B. Such dependence of V on [H2] can be analyzed by a Michaelis-Menten type equation,17 which is written, in the present case, by
Tatsumi et al.
Figure 1. (A) Current-time curve for the oxidation of H2 recorded with a Clark-type oxygen electrode at 0.6 V vs Ag|AgCl in D. Vulgaris (H) cell (1.4 × 10-13 M) suspension at pH 7.0. The suspension was made 1.4 mM in VK3 by the addition of VK3 at the point indicated by the arrow. (B) Plot of the rate, V, of the D. Vulgaris (H) cell-catalyzed H2 oxidation against the concentration of H2, [H2]. D. Vulgaris (H) cell: 1.4 × 10-13 M. [VK3]: 1.4 mM. Solid line is the regression curve by eq 1′ with the kB,cat and KB,H values given in Table 1.
V)
kB,cat[B] 1 + KB,H/[H2] + KB,Q/[Q]
(1)
where KB,H and KB,Q are the Michaelis constants for H2 and quinone (here VK3), respectively, and kB,cat is the catalytic constant of D. Vulgaris (H) cell. A simplified form of eq 1 (eq 1′): V ) kB,cat[B][H2]/(KB,H + [H2]) was used in analyzing the data in Figure 1B, since the reaction rate was almost independent of the quinone concentration [Q] (here [VK3]) under the experimental conditions. The two parameters kB,cat and KB,H were determined by adjusting them to give the best fit to the data by means of nonlinear curve fitting. The kB,cat and KB,H values thus determined are given in Table 1 and the result of the regression is illustrated by the solid curve in Figure 1B. In a similar manner, sets of kB,cat and KB,H values were determined for the D. Vulgaris (H) cell catalysis with DMBQ and NQ as electron acceptors and are given in Table 1. All the quinone compounds give similar kB,cat values, which is much higher than the catalytic constant 5 × 104 s-1 for a hydrogenase reaction calculated from the reported specific activity18 and molecular weight.19 Dependence of the Catalytic Reaction Rate on the Concentration of an Electron Acceptor. Catalytic currents due to quinone-mediated D. Vulgaris (H) cell-catalyzed oxidation of H2 were measured as described in the Experimental Section. Figure 2A depicts examples of the catalytic currents measured by potential step chronoamperometry under the condition
Fast Hydrogenase Reaction of DesulfoVibrio Vulgaris Cells
J. Phys. Chem. B, Vol. 104, No. 50, 2000 12081
TABLE 1: Kinetic Parameters for H2 Oxidation and Quinone Reduction Catalyzed by D. Vulgaris (H) Cells
i ) 2FA
electron acceptor redox potential/Va H2 oxidation kB,cat/107 s-1 KB,H/µM (kB,cat/KB,H)/ 1012 M-1 s-1 quinone reduction kB,cat/107 s-1 KB,Q/mM (kB,cat/KB,Q)/ 1010 M-1 s-1 a
DMBQ -0.02
NQ -0.15
VK3 -0.19
5.0 ( 0.5 27 ( 5 1.8 ( 0.3
5.3 ( 0.4 25 ( 4 2.1 ( 0.3
3.2 ( 0.3 15 ( 2 2.2 ( 0.3
AQS -0.42 N.D.b N.D.b N.D.b
1.1 ( 0.1 3.2 ( 0.2 4.2 ( 0.3 N.D.b 0.15 ( 0.02 0.31 ( 0.04 0.62 ( 0.05 N.D.b 7.5 ( 1.0 10 ( 1 6.8 ( 0.5 0.97 ( 0.05
vs Ag|AgCl. b N.D.; Not determined.
x
DQkB,cat[B]
KB,Q + [QH2]/2
‚ [QH2]/f
(2)
where F, A, and DQ are the Faraday constant, the electrode surface area, and the diffusion coefficient of quinone (here VK3), respectively, and f is a correction factor given by f ) 1 + ([QH2]/KB,Q)/{0.85([QH2]/KB,Q)2 + 11.4([QH2]/KB,Q) + 17.9}; [QH2] is the bulk concentration of the reduced form of quinone and can be equated to the initial value of [Q] (here [VK3]). The two parameter values, kB,cat and KB,Q, were determined by nonlinear curve fitting with the experimental value FA(DQ)1/2 ) 17.7 cm3 A s1/2 mol-1(from chronoamperometry of VK3 in the absence of D. Vulgaris (H) cells) and [B] ) 1.1 × 10-12 M. The kB,cat and KB,Q values are given in Table 1, and regression lines with them are depicted by the solid lines in Figure 2B. In the same way, values of kB,cat and KB,Q for the reactions with DMBQ and NQ were determined as given in Table 1. In the case of AQS, only the ratio kB,cat/KB,Q was able to be determined because only a linear portion of the plot like those in Figure 2B was obtainable owing to the low solubility of AQS. Table 1 reveals that the kB,cat values determined by the two different methods with a given quinone are in fairly good agreement with each other as required by eq 1. Discussion According to ordinary ping pong bi bi system,20 hydrogenase reaction is expressed as k1
k2
}H2‚Eox982H+ + Ered H2 + Eox{\ k -1
k3
(3)
k4
Ered + Q{\ }Ered‚Q98Eox + Q2-; Q2- + 2H+ ) QH2 (4) k -3
Figure 2. (A) Chronoamperograms of VK3 in H2 gas-saturated solutions in (a) the absence and (b-f) presence of 1.1 × 10-12 M D. Vulgaris (H) cell. Concentration of VK3: (a) 100, (b) 10, (c) 30, (d) 50, (e) 70, and (f) 100 µM. The potential was stepped from -0.35 V to 0.15 V vs Ag|AgCl. (B) Dependence of the steady-state current, i, on the concentration of VK3, [VK3]. Solid lines are the regression curves by eq 2 with the kB,cat and KB,Q values given in Table 1.
[H2] . KB,H. The broken curve in Figure 2A (a) is the current recorded at 0.10 mM VK3 in the absence of D. Vulgaris (H) cells, showing a cathodic current of significant magnitude attributable to the diffusion-controlled reduction of VK3. Curves b to f, on the contrary, exhibit no appreciable cathodic current, ensuring that VK3 was converted to the reduced state by the D. Vulgaris (H) cell-catalyzed reduction with H2 in the solution. Upon the potential step to 0.15 V, steady-state anodic currents are observed which are dependent on [VK3] as shown in Figure 2B. The nonlinear dependence of the current on [VK3] can be analyzed by eq 2,9 which describes the current due to a mediated enzyme electrocatalysis,15,16 to yield the values of kB,cat and KB,Q
where Eox and Ered are the oxidized and reduced forms of hydrogenase; Q and QH2 are a quinone compound and its reduced form, respectively; H2‚Eox and Ered‚Q are the substrateenzyme complexes. The rate constants of the respective steps are given by k1, k-1, k2, k3, k-3, and k4. The catalytic constant, kcat, and the Michaelis constants KH and KQ for the hydrogenase reaction are given by kcat ) k2k4/(k2 + k4), KH ) k4(k-1 + k2)/ k1(k2 + k4), and KQ ) k2(k-3 + k4)/k3(k2 + k4), respectively. The catalytic constant kB,cat for the bacterial catalysis (eq 1) would be related to kcat by kB,cat ) zkcat with z the number of hydrogenase molecules contained in a D. Vulgaris (H) cell as discussed previously.9 KB,H and KB,Q could reflect the effect of outer membrane permeability and can be equated with KH and KQ, respectively, provided that the mass transfer effect is not significant.17 It is noted that the values of the bimolecular reaction rate constants, kB,cat/KB,H, and kB,cat/KB,Q, (Table 1) are very large despite the involvement of the substrate mass transfer process in the bacterial cell-catalyzed reaction. Thus, the kinetic parameters could be affected by the rates of the substrate diffusion toward the cell surface and/or the substrate permeation through the bacterial outer membrane. The effect of this mass transfer process is examined in the following. An Expression for Outer Membrane Permeability. Gramnegative bacteria have proteins termed porins forming the crossmembrane channels in the outer membrane, through which small molecules can diffuse freely into the cytoplasmic space.21 Pore size of the porins isolated from E. coli has been evaluated as 1.1-1.9 nm in diameter and 6 nm in depth.22 On this basis, we assume a size of D. Vulgaris (H) porins as a cylindrical tube with a minimum radius, rp, 0.5 nm, and a length, lp, 6 nm as
12082 J. Phys. Chem. B, Vol. 104, No. 50, 2000
Tatsumi et al.
SCHEME 1: A Model of a Bacterial Cell with the Radius rB. Outer Membrane of the Cell Has Porins with the Radius rp and the Length lp
illustrated in Scheme 1. We consider the mass transfer to and through the pore by means of an analytical approach relying upon the theory of diffusion at a microdisk23,24 and in a planer sheet.25 The diffusion-controlled fluxes, fd and fl, to and through (from the inlet x ) 0 to the outlet x ) lp) the pore, can be written as
fd,x ) 0 ) Dc*[4/πrp + 0.81/(πDt)1/2 + 0.059rp2/(πDt)3/2 + ‚‚‚] (5) with the condition c ) 0 at x ) 0,24 and ∞
f1,x ) l ) (Dc*/lp)[1 + 2
∑(-1)n exp (-n2π2Dt/l2p)]
(6)
n)1
with the conditions c ) c* at x ) 0, c ) 0 at x ) lp, and c ) 0 at 0 < x < lp and t ) 0,25 where D and c* are the substrate diffusion coefficient and its concentration in the bulk, respectively. These equations predict that fd,x ) 0 and f1,x ) l approach steady states when 1.57(πDt)1/2 . rp and π(Dt)1/2 . lp, that is when t . 64 ps for fd, x ) 0 and t . 7.3 ns for f1, x ) l with, e.g., D ) 5 × 10-6 cm2 s-1; thus, the fluxes are in the steady state under the present experimental conditions. The amounts of substance diffusing to, Md, and through, Ml, the pore per second are given in the steady state by Md ) 4rpDc* and Ml ) πrp2l-1 p Dc*. Then, the total amount of diffusing substance per D. Vulgaris (H) cell is given by the product of Md (or Ml) and the number of pores in the outer membrane, np. A probable np value can be estimated as (6-12) × 104 if we assume that the pores are distributed with the density 2-4 pores per 100 nm2 on the outer membrane surface (a schematic model of a bacterial outer membrane is given in ref 21) and that D. Vulgaris (H) cell has a spherical surface with the radius rB ) 0.5 µm (the bacterial cell has actually an ellipsoidal shape of the dimension about 0.5 µm × 2.0 µm).21 Thus, npMd and npM1 are calculated to be npMd ) (1.2-2.4) × 10-2Dc* and npM1 ) (0.79-1.6) × 10-3Dc*. Substrate Diffusion toward the Bacterial Cell Surface. Diffusion-controlled flux to the spherical cell surface, fB, (Scheme 1) is written by fB ) Dc*[1/(πDt)1/2 + 1/rB].26 It approaches a steady state when (πDt)1/2 . rB, that is, when t . 0.16 ms with rB ) 0.5 µm and with a tentative D value of 5 × 10-6 cm2 s-1. In the steady state, the amount of substance diffusing to the cell surface per second, MB, is given by 4πrBDc*, which is calculated to be MB ) 6.3 × 10-4Dc*.
Interestingly, the MB value is smaller than those of npMd and npM1. It should be noted, however, that at sufficiently long times the flux fd is no longer described by eq 5 owing to the overlap of the diffusion layer formed at a porin with those formed at adjacent porins. The total flux npfd at sufficiently long times is now described as the flux to the total surface area of the bacterial cell, that is fB, as is the case for the flux to an ensemble of microdisk electrodes.27,28 Thus, npMd is reduced to MB in the steady state. Effect of the Mass Transfer Rates on the Rates of the Bacterial Cell-Catalyzed Reaction. When the bimolecular reaction rate constants, kB,cat/KB,H, and kB,cat/KB,Q, are to be compared with the values of MB and npM1, the rate constants must be converted to the quantities corresponding to the amount of substrate subjected to the reaction with a bacterial cell per second. This can be done by multiplying 1000c*/NA (NA being the Avogadro constant) to yield the quantities Mcat,H ) 1000kB,catc*/NAKB,H and Mcat,Q ) 1000kB,catc*/NAKB,Q with the dimension of mol s-1, where c* is the bulk concentration of hydrogen or quinone expressed in mol cm-3. The Mcat,H and Mcat,Q values are calculated to be Mcat,H ) 3.5 × 10-9c* and Mcat,Q ) 1.7 × 10-10c* with the kB,cat/KB,H and kB,cat/KB,Q values in Table 1 (kB,cat/KB,H ) 2.1 × 1012 M-1 s-1 and kB,cat/KB,Q ) 1.0 × 1011 M-1 s-1 for NQ). They should express the rates of the overall catalytic reaction involving the mass transfer process, and are related to MB and npM1 and the rate of the true bimolecular reaction, M, by
1/Mcat,H (or 1/Mcat,Q) ) 1/MB + 1/npM1 + 1/M
(7)
Rearrangement of eq 7 leads to Mcat,H/M ) 1 - (Mcat,H/MB + Mcat,H/npM1). The quantities Mcat,H/MB and Mcat,H/npM1 are readily calculated with D ) 2.4 × 10-5 cm2 s-1 for H2 29 as Mcat,H/MB ) 0.23 and Mcat,H/npM1 ) 0.091-0.18. Thus, the effect of the mass transfer rate is evaluated as 32-41% for H2. In the same way, the effect of the mass transfer rate for NQ is evaluated as 4.7-6.1% with Mcat,Q/MB ) 0.034 and Mcat,Q/ npM1 ) 0.013-0.027 (D ) 8.0 × 10-6 cm2 s-1 for NQ determined by chronoamperometry). The calculation reveals that the rate of the diffusion toward the cell surface is slower than that of the diffusion through the cross-membrane channels. Since the npM1 value used here was calculated with a minimum value of rp (rp ) 0.5 nm) as mentioned above, the actual npM1 value would be somewhat larger, and thus, the ratios Mcat,H/npM1 and Mcat,Q/npM1 are expected to be even smaller than those calculated above. The calculation also reveals that the rate of the H2 diffusion toward the cell surface is only four times the rate of the bacterial catalytic oxidation of H2. Although the MB value was calculated on the basis of a spherical diffusion model despite an ellipsoidal shape of the bacterial cell, the result indicates that the D. Vulgaris (H) cell-catalyzed oxidation of hydrogen with exogenous quinones proceeds at the rate comparable to that of diffusion-controlled reaction. Finally, it should be mentioned that the present result does not necessarily mean a possibility of the D. Vulgaris (H) cell catalysis at a diffusioncontrolled rate in a practical application, e.g., in a fuel cell system, in which the cell catalysis is operated under high substrate concentrations. The catalytic reaction rate under high substrate concentrations is determined by kB,cat and no longer diffusion-controlled owing to the nonlinear kinetics given by eq 1. Acknowledgment. This research has been supported in part by a grant from Kansai Research Foundation for Technology Promotion.
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